In which of the following intervals the inequality, `sinx < cos x < tanx < cot x` can hold good ?
In which of the following intervals the inequality, `sinx < cos x < tanx < cot x` can hold good ?
A. `((7pi)/4,2pi)`
B. `((3pi)/4,pi)`
C. `((5pi)/4,(3pi)/2)`
D. `(0,(pi)/2)`
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Correct Answer - D
In the second quadrant, `sinxltcosx` is false, as sinx is positive and cosx is negative.
In the third quadrant, i.e., `((5pi)/4,(3pi)/2)` is tanx lt cotx then `tan^2xlt1`, which is false.
Now,`sinxltcosx" is true in "(0,pi/4)` and tanxltcotx is also true.
Further, cosx lt cotx, as `cotx=cosx/sinx and sinxlt1`.
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